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Mirrors > Home > ILE Home > Th. List > sb4bor | Unicode version |
Description: Simplified definition of substitution when variables are distinct, expressed via disjunction. (Contributed by Jim Kingdon, 18-Mar-2018.) |
Ref | Expression |
---|---|
sb4bor |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb4or 1844 |
. 2
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2 | sb2 1778 |
. . . . 5
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3 | df-bi 117 |
. . . . . 6
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4 | 3 | simpri 113 |
. . . . 5
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5 | 2, 4 | mpan2 425 |
. . . 4
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6 | 5 | alimi 1466 |
. . 3
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7 | 6 | orim2i 762 |
. 2
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8 | 1, 7 | ax-mp 5 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: (None) |
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